(Just need the second answer)

Answer:

There are two possible solutions:

Clockwise rotation

[tex]P'(x,y) = (-10,5)[/tex]

Counterclockwise rotation

[tex]P'(x,y) = (10, -5)[/tex]

Step-by-step explanation:

There are two possible answers: (i) Clockwise rotation, (ii) Counterclockwise rotation. Vectorially speaking, rotation of point of rotation of a point about another point of reference is defined by:

[tex]P'(x,y) = O(x,y) + r_{OP}\cdot (\cos (\theta_{OP}\pm \theta'),\sin (\theta_{OP}\pm \theta'))[/tex] (1)

Where:

[tex]O(x,y)[/tex] - Point of reference.

[tex]r_{OP}[/tex] - Length of the segment OP.

[tex]\theta_{OP}[/tex] - Direction of segment OP, measured in sexagesimal degrees.

[tex]\theta '[/tex] - Angle of rotation, measured in sexagesimal degrees.

Please notice that clockiwise rotation occurs when [tex]\theta = \theta_{OP}-\theta'[/tex] and counterclockwise rotation when [tex]\theta = \theta_{OP}+\theta'[/tex]. In addition, we define length and direction of the segment below:

[tex]r_{OP} = \sqrt{(x_{P}-x_{O})^{2}+(y_{P}-y_{O})^{2}}[/tex] (1)

[tex]\theta_{OP} = \tan^{-1} \frac{y_{P}-y_{O}}{x_{P}-x_{O}}[/tex]

If we know that [tex]x_{O} = y_{O} = 0[/tex], [tex]x_{P} = 5[/tex], [tex]y_{P} = 10[/tex] and [tex]\theta' = 270^{\circ}[/tex], then the coordinates of the first car after rotation is:

[tex]r_{OP} = \sqrt{(5-0)^{2}+(10-0)^{2}}[/tex]

[tex]r_{OP} \approx 11.180[/tex]

Please notice that original point is located at first quadrant of the Cartesian plane centered at origin, then the direction of the segment OP is:

[tex]\theta_{OP} = \tan^{-1} \frac{10-0}{5-0}[/tex]

[tex]\theta_{OP} \approx 63.435^{\circ}[/tex]

The two solutions are finally presented:

Clockwise rotation

[tex]P'(x,y) = (0,0) + 11.180\cdot (\cos (-206.565^{\circ}),\sin (-206.565^{\circ}))[/tex]

[tex]P'(x,y) = (-10,5)[/tex]

Counterclockwise rotation

[tex]P'(x,y) = (0,0) + 11.180\cdot (\cos (333.435^{\circ}),\sin (333.435^{\circ}))[/tex]

[tex]P'(x,y) = (10, -5)[/tex]

Answer: Rs. 1,650

Step-by-step explanation:

First find the original price of the watch.

If the watch is sold at Rs. 1,275, there is a 15% loss.

Assume the watch is x.

(1 - 15%) * x = 1,275

0.85x = 1,275

x = 1,275 / 0.85

x = Rs. 1,500

Now add a 10% markup on the original:

= (1 + 10%) * 1,500

= 1.1 * 1,500

= Rs. 1,650

Answer:

Answer for the first pic is 122.24  

Answer for the second pic is A

Step-by-step explanation:

the rectangle is 72 in

the semi-circle is 50.24

Answer for the first pic: 122.24 in  

Answer for the second pic: A

Answer:

31.0

Step-by-step explanation:

The mean of a given set of data is the ratio of the sum of the data to the number of units that make up the data set. It is also called the average of the data set.

Given the data set {22, 34, 37, 23, 45, 21, 29, 37}. There are 8 numbers in the set. The total of these numbers

= 22 + 34 + 37 + 23 + 45 + 21 + 29 + 37

= 248

The mean = 248/8

= 31

Answer:

4900

Step-by-step explanation:

so what you're going to do first is you're going to do 114* 43 which equals 4902 then you round that and you're going to have 4900I am not a hundred percent sure

G I V E N

Speed of driver = 5 miles/hours

Distance to be covered = 62.8 miles

F O R M U L A  ~  U S E D

Speed = Distance/Time

S O L U T I O N

Time = Distance/Speed

= 62.8 miles / 5 miles / hour

= 12.56 hours

It will take 12.56 hours to cover 62.8 miles, if the driver is moving

with 5 miles/hours

Answer:D!

Step-by-step explanation: i’m taking the test rn!

Answer:

The answer is 9

Step-by-step explanation:

27^2 =729

729/27^4/3

Answer:

I simplified it to -20x - 35

Step-by-step explanation:

-5 times 4x is -20x, -5 times 7 is -35.

Solution :

The amount invested by Yvonne = $ 4,000

Time of investment = 3 years

The simple interest earned by Yvonne in 3 years = $ 960

a). Therefore, the amount Yvonne earned by the end of three years is

= principal + interest earned

= 4,000 + 960

= $ 4,960

b). The formula for simple interest(S.I.) is given by :

   [tex]$S.I. =\frac{P.T.R}{100}$[/tex]

  or [tex]$R = \frac{SI \times 100}{P.T}$[/tex]

          [tex]$ = \frac{960 \times 100}{4000 \times 3}$[/tex]

          = 8%

c). Now if the interest rate is 1% greater, i.e. R = (8+1) = 9%

   ∴ [tex]$SI =\frac{P.T.R}{100}$[/tex]

      [tex]$SI =\frac{4000 \times 3 \times 9}{100}$[/tex]  

      SI = $1,080

Therefore, the amount at the end of 3 years with 9% rate of interest will be

  = 4000 + 1080

  = $ 5080

Thus, Yvonne will have 5080 - 4960 = $ 120 money more in her account if the rate of interest was 1% greater.

Answer:

A. V13

Step-by-step explanation:

Step-by-step explanation:

since it is a circle the diameter is two times larger than radius.So 4×2=8km

Answer:

The answer would be 5

Step-by-step explanation: Plz mark brianliest

Answer:

нечего не понятно но очень интересно да, очень

Answer:

p=22

sooooooooooooooooo ezzzzzzzzzzzzzzzzzzzzz

Answer:

12mlies

Step-by-step explanation:

just add 7 + 5 and boom you have you answer

Answer:

5 times

Step-by-step explanation:

5*5 is 25

40-25=15$ left

any more movie tickets would be too much money spent

If Robin was given a $40 monthly allowance. She wants to go to the movies as many times as possible and have at least $12.50 left at the end of the month to go to a concert. A movie ticket costs $5. Then she can go six times to the movies.

Two or more expressions with an Equal sign is called as Equation.

Given,

Robin was given a $40 monthly allowance.

She wants to go to the movies as many times as possible and have at least $12.50 left at the end of the month to go to a concert.

The amount spent on movies

40-12.5

$27.5

A movie ticket costs $5.

We need to find how many times can she go to the movies.

To find this we need to divide $27.5 by 5

$27.5/5=5.5

Robin can go 6 times to the movies.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ5

Answer:

-234

Step-by-step explanation:

5x + 4y =8 2x -3y = 17 -3 O -2 O 4 O5=234

Answer:

The Independent is the Number of Hours while the Dependent is the Number of Miles

Equation: y= 50x

Step-by-step explanation:

I Hope this helped

Answer:

-3x + 36

Step-by-step explanation:

Answer:

[tex]\displaystyle EF \approx 15.9[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

Angle θ = 28°

Adjacent Leg = EF = x

Hypotenuse = DF = 18

Step 2: Solve for x

Since chad was charged 1 dollars for each hour for 6 hours, we can represent this as 1 x 6. Now subtract 6 dollars from the bill for the hours and it leaves the initial fee of $4 for rental.

Now check your work:

(1 x 6) + 4 = 10

Answer:

They would pay $28.

Step-by-step explanation:

4 x 3 = 12, 22-12= 10. $10 is initial fee.

6 x 3 = 18, 18+10= 28. $28 for 6 hours

Answer:

slope = 2, y- intercept = - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 4 + 2x , that is

y = 2x - 4 ← is in slope- intercept form

with slope m = 2 and y- intercept c = - 4

Answer:

[see below]

Step-by-step explanation:

50 apples cost 25 dollars.

25/50 = 0.5

Each apple cost half a dollar.

0.5 * 75 = 37.50

75 apples should cost $37.50.

Hope this helps.

Answer:

I believe it's eighteen.

Step-by-step explanation: